20IO 3rd International Conference on Advanced Computer Theory and Engineering(ICACTE)

The fault diagnosis for centrifugal compressor based on time series analysis with neutral network

LIAO Hong-Jian, HUANG Sheng-Zhong Department of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi 545004, China

gxhsz@126.com, lhj 181275@163.com

Abstract-In order to have fault diagnosis for centrifugal compressor correctly, the times series analysis with neural network was carried out for it. The theory model of time series analysis method was put forward firstly, and the autoregressive coefficients diagnosis method was discussed then. And the neural network diagnosis method with AR coefficients was put forward at last. And the fault diagnosis results of centrifugal compressor were acquired based on BPNN and distance diagnosis method, and diagnosis results was good.

Keywords-fault diagnosis, centrifugal compressor, BPNN

I. INTRODUCTION

The fault diagnosis in centrifugal compressor was defined as applying vibration signals to identify fault types depending on expert's knowledge when the centrifugal compressor destroyed; Because the vibration signals included the critical characteristics or helpful feature when the centrifugal compressor was working, it was necessary to find out the characters of vibration signals by using accelerometers and applied these characters to identify fault types based on artificial affect for traditional fault diagnosis means. Because the dissimilar fault modes had dissimilar frequency spectrum distributions, the fault diagnosis results were depended on frequency characters of vibration signals. A scientist gathered frequency spectrum of vibration signals from the destructive electrical centrifugal compressors to sort out fault modes depended on the association between amplitude of frequency characters and fault modes. Some scientists applied frequency spectrum means to confirm gear faults of the gearbox system. Because the association matrix of frequency characters and fault modes was complicated, it was difficult to confirm fault modes by this matrix with human intervene, and different disparate outcomes were distinctive with dissimilar expert's experience. The conventional diagnosis means for example fuzzy deduce and approach means should be affected by human forejudge and experience and the value of weighting parameters was also designed by human thought. As the regulations given or defined by all kinds of experts were different, the diagnosis results were not concordant. In addition, the relation matrix was hard to deal with if the amount of characters and fault modes were very large. Lately, artificial neural network was widely used in mode identification and classification realms. There were some strong points of artificial neural network, for example the weightings of neural network were acquired from neural calculating and the fault diagnosis results

depended on artificial neural network were objective than traditional means.

Back-propagation neural network (BPNN) was a kind of neural network and was applied widely in dealing with fault diagnosis researches. Some scientists came down on fourteen noisy measurement characters and ten faults as inputs and outputs of neural network, respectively, and applied multilayer perception network with a hyperbolic tangent to identify faults in a realistic heat exchanger continuous stirred tank reactor system. Some scientists applied frequency characters of the rolling bearings as inputs of neural network to diagnosis bearing defect types in motor­bearing system. A lot of scientists collected frequency characters of vibration signals to find out faults depended on fuzzy neural network (FNN) in motor-bearing system and acquired good diagnosis results. Despite the perfect diagnosis results could be acquired by BPNN or FNN with frequency characters, the vibration signals could be misrepresented when the signals were windowed in Fourier transfer. The distribution of frequency spectrum was not clear for the shock vibration signals. Besides, there are frequency sideband distributions in frequency modulation condition, it is difficult to determine true features, and thus diagnosis results were not satisfactory with human being's diagnosis results. As the relation matrix between frequency features and fault types was established by expert' s knowledge or experiments, the accuracy of diagnosis results was affected by this relation matrix. The above shortcomings were solved by using time series analysis. The common method used in time series analysis is the autoregressive analysis method. The autoregressive (AR) analysis used time variations and vibration amplitude to establish the math model for regression and forecast.

Because the AR model was established by using variables fitling, there are filter and noise suppression ability in signal processing. Some amended the disadvantages of distortion and low resolution by using AR spectrum in medicine diagnosis. Otherwise, the AR coefficients were used to determine the fault types. Some scientists presented the AR model of inner race defect, outer race defect and normal bearing with the same orders, respectively. Although there are no variables needed to classify fault types with the other distance method, such as Euclidean distance method, it would cause computation complexity and spend more diagnosis time for large relation matrix between features and faults. The relationship between AR coefficients and fault types was trained by learning and recalling ability of BPNN and was used to determine faults types. Two scientists founded the AR model of inner race defect, outer race defect,

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2010 3rd International Conference on Advanced Computer Theory and Engineering(ICACTE)

ball bearing defect and normal bearing with the different orders. The AR coefficients were used to train samples by using neural network. Because each AR model had different AR orders, the four kinds of AR model were established dependently. In fault diagnosis, the AR coefficients were computed with different orders dependently and were used to identifY fault modes with neural network. The value of output neuron of neural network indicated the possibility of bearing faults.

Because the rotary speed occurred necessarily when centrifugal compressor was running, this study proposed the difference of AR coefficients, which means that the AR coefficients of ideal signal for normal centrifugal compressor were deducted from the faulty centrifugal compressor. The relationship between difference of AR coefficients and fault types was trained by applying neural network. In this research, the diagnosis results acquired by using neural network with difference of AR coefficients were improved and were superior to results that were acquired by using neural network with AR coefficients and distance methods.

II. TIME SERIES ANALYSIS METHOD

(1) Autoregressive moving average model Autoregressive moving average (ARMA) model was a

kind of math regressive method to set up the variables relationship. The ARMA (n, m) model could be expressed as

� -lfII�-1 -... -lfIny"-1 = b, -f}lbl_l - . . . - f}mb, _ m (1)

where � -�-n and b, -b,_m were n+ 1 independent and m+ 1

dependent variables before time t, respectively. lfII -lfl nand

f}l - f} m were coefficients of independent (AR) and

dependent (MA) variables, respectively, n and m were orders of AR and MA, respectively, and was the residual squared error, which was the squared error summation between the prediction and ideal variables. (2) AR model of fault diagnosis

AR (n) model with time-domain vibration signals for fault diagnosis could be expressed as

� = lfIl �-l + ... + lfI n�-n + b, (2)

where � - �-n were time-domain vibration signals, lfIl­lfI n were n order AR coefficients. The nth order of AR model matrix with N number points of time-domain vibration signals could be written as

Z = YA+a2 (3) Where

� �-l �-2 �-n

Z= �+l Y= � �-l �+l-n (4)

YN YN-1 YN-2 YN-n

lfI, b,

A= lfI2 a2 bl+1 (5)

lfIn b N where A and a2 were AR coefficients set and residual squared error, respectively. Each of AR coefficients set could be considered as the features of vibration signal. The AR coefficients set was able to be computed by using minimum squared error (MSE) method, and equation could be expressed as

A = (y'Y)-1 X'Z (6) Substituting the AR coefficients into Eq. (2) and

computing the residual squared error, the formula could be expressed as

N N La; = L(Yk -lfIIYk-1 -" ' + lfInYk_n ) 2 (7) k=1 k=1 If the value of residual squared error approach zero,

which showed that the AR model would be more precision and the AR coefficients could be widely applied for characters in the theory model.

III. AUTOREGRESSIVE COEFFICIENTS DIAGNOSIS METHOD

(1) The AR coefficients distances diagnosis method The AR coefficients distances diagnosis method applied

the distance values, which computed between AR coefficients sets of test and trained samples to determine the fault types. The common distance diagnosis method was the Euclidean distance and could be expressed as

n h, = L (lfIi' -lfIi,,\,)2 , i = 1,2,3 . . · , n (8)

where hs showed the Euclidean distance of AR coefficients

set between the test and sth trained sample. lfIi is the ith

order normalized AR coefficient in the test sample, lfIi,s is

the ith order normalized AR coefficient of the sth trained AR coefficient sample in the relation matrix, n was the

order of the AR model. If the distance hs was small, it

showed that the two samples were similar and also had the same fault type. (2) The neural network diagnosis method with AR coefficients

The AR model was established by time-domain vibration

signals, and AR coefficients lfIi,S were obtained by using

minimum squared error (MSE) method. Each of the AR coefficients of fault was normalized and can be written as

lfIi \' " lfI i,s -lfI min,s (9) ,i = 1,2,3· . . ,n

lJf max,s -lfI min,s

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2010 3rd International Conference on Advanced Computer Theory and Engineering(ICACTE)

where i is the order of AR coefficient, s is the fault type,

If/i,s indicated the ith order AR coefficients of the sth

training sample, If/i,s indicated the ith order normalized AR

coefficients of the sth training sample, If/ max,s and If/ min,s

are the maximum and minimum AR coefficients of the sth training sample. Because the order of AR model is equal to the number of input neurons in BPNN and sequentially corresponds to the same input nodes of BPNN of the same

order, in Fig. I, the ith input neuron OUTPUT; = If/i,s and

the output neuron OUTPU� - OUTPU� , which

indicated the k kind of fault types. eij is the weighting

coefficients between the ith neuron in the input layer and the

jth neuron in the hidden layer. ejk is the weighting

coefficients between the jth neuron in the hidden layer and the kth neuron in the output layer. The input of the jth neuron in the hidden layer can be expressed by

n

nj = �>ijLi (10) i=1

where Ii is the ith neuron of input layer. The jth output neuron in the hidden layer can be expressed by

Dj = fen) (11)

Figure 1 the diagram of neutral network where f (.) is the sigmoid function adopted to be the activation function. The output neuron of BPNN can be expressed by k

nk = L wjkDj (12) j=l

where k is the neuron number of the output layer. Then, the output neuron Outputk of the BPNN can be expressed by

1 OUTPU� = f(nk) = (13)

1 + exp(-nk)

IV. CASE STUDY

In this research, the AR coefficients and its difference values were applied to study samples by applying BPNN

and identified fault modes and were contracted with the distance of AR coefficients means. The 34 time-domain vibration signals were measured from accelerometer that fixed on the bearing house of centrifugal compressor when large-scale centrifugal compressor was operating. In which, the 11 AR coefficients were applied for training samples of BPNN, the other 10 AR coefficients were applied for verifying samples.

The 10 normalized AR coefficients

If/i,,(i = 1-15,s = 1-10) and its difference value di,s set sequentially corresponding to the similar input nodes of BPNN of the same order, respectively.

The 15 orders of AR coefficients were applied for neurons of input layer in BPNN, and the neurons value of

hidden layer was 25. The neurons OUTPU� -

OUTPUT4 of output layer in BPNN were showed four

different kinds of fault modes. The ascertained faults were represented with value 1, and un-happened faults were represented with value O. For example, the fault type is unbalanced in serial number 1 of training sample; the fault mode was multiple faults concluded with unbalance of the rotor, failure of thrust bearing, oil whipping and surging condition in serial value four of training sample.

The BPNN was trained using the error between the real

output and the ideal output, to change coefficients eij and

ejk until the output of BPNN was near to the ideal output,

with simulating error 0.001. When the network training was

completed, the weighting coefficients eij and ejk were

applied for connection between AR coefficients and fault modes. The fault diagnosis results were acquired by using BPNN and were shown in Tables 1.

Tables 1 The fault diagnosis results of centrifugal compressor

Training sample

2 3 4 5 6 7 8 9

10

Fault types Unbalance Failure oil of the rotor of thrust whipping

bearing 0 0.9948 0 0 0 0.9929

0.9958 0 0.9985 0.9949 0.9918 0.9968

1 1 0 0 1 0 0 0.9943 0

0.9899 0 0.9921 0.9839 0 0 0.0012 0.9853 0

V. CONCLUSIONS

surging condition

0 0 0 0 0 1 0 0

0.9983 0.9848

In this research, the diagnosis results of the ten test samples were acquired based on BPNN and distance diagnosis method. The diagnosis results were ideal and the

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computation is single. The diagnosis results by using the difference value of AR coefficients with BPNN were good through simulation samples.

REFERENCES

[1] Kang, Y., Wang, C. c., Chang, Y. P., "Certainty improvement in diagnosis of multiple faults by using versatile membership functions for fuzzy neural networks," Lecture Notes in Computer Science, 2006, 147.

[2] Wang, W., & Wong, A. K., "Autoregressive model-based gear fault diagnosis," Journal of Vibration and Acoustics, Transactions of the ASME, 2002, 124(2).

[3] YUAN Jing , XU Yu-xiu , QIAO Guo-dong, "Application of wavelet and BP neural-net in fault diagnosis of engine gases distributing system," Journal of Tianjin Polytechnic University. 2009, 128(4).

[4] PENG Tao, MA Qian., "Application of wavelet neural network on rolling element bearings fault diagnosis", Computer Engineering and Application, 201 0, 46(4).

[5] Chen Chang-zheng, Gou Yi, Wang Y., "Mechano-electric system fault diagnosis based on wavelet analysis and neural networks", IEEE Eleetrical Centrifugal compressors and System, 2005, 9(3)

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